The present invention relates to apparatus for determining the common frequency w of two independently variable electrical a-c quantities denoted herein a.sub.1 and a.sub.2, wherein an angle quantity .alpha. varying with frequency w is associated with the a-c quantities a.sub.1 and a.sub.2 according to the relation a.sub.1 /a.sub.2 =cotan .alpha..
A preferred field of application of the invention is the field-oriented control or regulation of a rotating-field machine drive. As used herein, rotating field machines comprise both synchronous and asynchronous machines. Such a drive comprises a rotating-field machine having power fed from a static frequency converter with apparatus for controlling or regulating the converter. This apparatus requires as an input control variable an angle which can be determined in a flux-determining device and which describes the instantaneous direction of the field axis, (for instance, in the form of two a-c variables sin .alpha., cos .alpha., where .alpha. may be the angle between the field axis and the axis of the stator winding). Furthermore, reference values are also inputs to the control apparatus which determine the components of the stator magnetization of the stator current parallel to the field axis and perpendicular thereto. With the component parallel to the field, the magnitude of the field can be set to a value, in particular, a constant value which is an optimum for the utilization of the frequency converter and the rotating-field machine, while independently thereof, the torque and the speed can be set by the field-parallel component in accordance with the requirements of the drive.
Such a drive is described in U.S. Pat. No. 4,282,473, corresponding to German Pat. No. 28 33 542 and in U.S. Ser. No. 279,352 filed July 1, 1981, corresponding to German patent Application No. P 30 26 202.3, all commonly owned by the assignee of this application, wherein the flux determining device determines, first, from stator currents and stator voltages, two electrical variables which are related to the EMF of the machine. By integration, the two electrical variables are determined from which the field with respect to the above-mentioned angle .alpha. as well as the magnitude of the field can be determined. This flux-determining device utilizes the instantaneous operating frequency w to provide, by setting a frequency-dependent amplification parameter, an adaptation to the respective operating state and ultimately, optimum attenuation of disturbing harmonics at any operating frequency. An adaptation to the prevailing operating frequency can advantageously also be made at other points of the machine drive. In the steady state, the operating frequency of a synchronous machine, for instance, is equal to the frequency of the rotating field, so that on occasion, the machine frequency itself has been used even where it would have been better to use the frequency of the rotating field.
The resulting electric magnetization of the stator which is determined by the current components of the individual stator windings, or the resultant stator current, can be represented by two variables a.sub.1 and a.sub.2 which determine the angle of the magnetization axis relative to a stationary axis, for instance, the axis of a stator winding. By the quantity c=.sqroot.a.sub.1.sup.2 +a.sub.2.sup.2, the magnitude of the electric flux linkage can be determined. The desired direction .alpha.* of the stator current can thereby be formed from two set values a.sub.1 *, a.sub.2 * for the stator current which are derived from the aforementioned reference values for the field parallel and field perpendicular stator current components and can be recalculated into the reference values i.sub.a *, i.sub.b *, i.sub.c * for the stator currents in accordance with EQU i.sub.a *=a.sub.1, EQU i.sub.b *=-1/2 a.sub.1 +.sqroot.3/2 a.sub.2, EQU i.sub.c *=-1/2 a.sub.1 -.sqroot.3/2 a.sub.2,
or the actual stator current can be described by the two a-c variables a.sub.1, a.sub.2 which are obtained from two actual stator winding values by reversing these relations.
It may also be advantageous to determine the change in direction of the total magnetization, i.e., the frequency at which, for instance, the angle between the stator current and the stationary reference axis changes from the predetermined or measurement-wise accessible a-c variables a.sub.1 and a.sub.2. Since in field-oriented operation, the current components which are parallel and perpendicular to the field, respectively, are given independently of each other, the a-c quantities a.sub.1 and a.sub.2 also are accordingly variable; the frequency w=d.alpha./dt therefore depends not only on one a-c quantity and its change in time, but also on the other a-c quantity (or the amplitude c) and its change. Due to these dependencies it can be expected that the frequency of change of the angle .alpha. can be calculated only with a relatively high cost apparatus.
Determination of the change of direction (for instance, the frequency of rotation relative to the rotor shaft) of the field and of the electric stator magnetization of a rotating-field machine, are only two conspicuous applications for the problem which occurs frequently in three-phase technology, namely, determination of the common frequency w from two a-c quantities a.sub.1 and a.sub.2 which depend via an angle variable .alpha. (for instance, a phase difference) variable with the frequency w according to the relation a.sub.2 /a.sub.1 =tan .alpha..
Although this frequency w depends on the a-c quantities themselves and also on the changes in time thereof as already mentioned, the use of differentiating circuits is not appropriate for determining the frequency w because differentiating circuits have only a limited computing range, which is quickly exceeded if the input variables have heavy harmonics or change in almost step-like fashion. In addition, differentiating circuits necessarily cause phase errors which lead to disturbing calculation errors, especially at high speeds of rotation.
It is therefore an object of the present invention to provide an apparatus for determining the common frequency w of two independently variable a-c variables.
It is a further object to provide such an apparatus which can be used in conjunction with a rotating field machine drive.
It is yet a further object to provide such an apparatus which avoids the use of differentiating stages.